Lewinsky, now 40 years old, resurfaced recently with an essay in Vanity Fair about how she has been unable to move past that time in her life and had trouble finding work because of the notoriety that came with what happened.

Letterman, who made his fair share of Lewinsky jokes back during the scandal, did something few late-night hosts do anymore. He seemed to express real regret about his role in making Lewinsky a household punch line.

"I started to feel bad, because myself, and other people with shows like this, made relentless jokes about the poor woman. And she was a kid!" Letterman said.

"With some perspective, you realize this is a sad human situation," Letterman said.

Walters pointed out that the Clintons have both been able to move on. But "Monica is still stuck in the humor of it," she said.

Walters then pointed out that Lewinsky has even thought about how to talk to her children about the incident, which clearly seemed to dig at Letterman, who has a son of his own.

It could also have something to do with his own life. In 2009, Letterman publicly announced he had once been involved with female staffers at his own show. The media soon revealed the identity of one of those women, his personal assistant, Stephanie Birkitt; a man she had once lived with attempted to blackmail Letterman. After Letterman’s public admission, Birkitt was quickly put on paid leave of absence from the show.

"Late Show with David Letterman" has seen it all. Click through the nostalgia.

(By Christy Khoshaba)

Watching David Letterman as he moves into his final year as a late-night TV show host continues to be an enlightening experience as the comedian's interviews appear less scripted and more soul-searching than at any time in his decades-long broadcasting history.

But when it came to Lewinsky's lack of meaningful employment, Letterman tried to enlist Walters' help.

"Would you ever have considered putting her on 'The View'?" Letterman asked.

That clearly brought a level of discomfort to Walters, who appeared like she wanted to answer one way, but couldn't in a public forum.

"Umm, I won't tell you what we have done, but it would have been possible," Walters answered cryptically.